Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 35 for “"Large deviation"”.
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Large deviation theory for queueing systems
… the population of at least one queue reaches a large number before becoming empty again is one and the typical sample trajectory of this event is another. To answer these questions, we establish the large deviation principle (LDP) for an appropriate class of queueing processes. The model of our …
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Large Deviation Local Limit Theorems for Ratio Statistics
<p>Let {T„, n > 1} be an arbitrary sequence of non-lattice random variables and {S<sub>n</sub>, n > 1} be another sequence of positive non-lattice random variables. Let the two sequences be independent. Let Ø<sub>1n</sub> and Ø<sub>2n</sub> be the moment genereating functions of {Tn, n > 1} and { …
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Design of Sensor Networks for Detection Applications via Large -Deviation Theory
… regimes where the number of nodes becomes large are important tools in identifying design guidelines for future sensor systems. This work presents interesting applications of large-deviation theory and asymptotic analysis to the design of wireless sensor systems in the context of …
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Large-deviation analysis and applications Of learning tree-structured graphical models
… We leverage this algorithm and the theory of large deviations to derive the error exponent of structure learning for discrete and Gaussian graphical models. We determine the extremal tree structures for learning, that is, the structures that lead to the highest and lowest exponents. We prove …
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Some aspects of empirical likelihood
… to the thesis. In chapter 2, Basics of Large Deviation Theory, we illustrate the basic idea of large deviation theory and briefly review the history of its development. As a preparation, some of the important theorems which we will employ in the following chapters are also …
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Kac's process and some probabilistic aspects of the Boltzmann equation
… of the same problem to show that the expected deviation between the Kac process and the Boltzmann equation, measured in expected Wasserstein distance, is of the order $N^{-\alpha}$. Particular care is paid to the time-dependence of the estimates, using the stability properties of the Boltzmann …
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Theory and applications of nonparametric regression in item response theory
… as both test length and sample size increase. A large deviation probability inequality is given for ordinal ability estimation. The mean squared error of kernel smoothed item characteristic curve estimates is studied and a strong consistency result is obtained showing that the worst case error in …
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A study of local approximations in information theory
… thereby linearizing such problems. We show that large classes of statistical divergence measures, such as f-divergences and Bregman divergences, can be approximated in an analogous manner to local metrics which are very similar in form. We then capture the cost of making local approximations of …
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ON SOLVING MULTI-OBJECTIVE SIMULATION OPTIMIZATION BY OPTIMAL COMPUTING BUDGET ALLOCATION AND RANDOM SEARCH
For decision-making in large-scale complex stochastic systems considering multiple conflicting objectives, analytical models and closed-form optimal solutions are usually hard to formulate and derive. These issues can be addressed by multi-objective simulation optimization, which employs efficient …
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Information theoretic limits of metagenomic binning
… Markov processes, where M ≪ N. Utilizing the large-deviation principle for Markov processes, we establish the information-theoretic limit for perfect binning. Specifically, we show that the length of the contigs must scale with the inverse of the Chernoff Information between the two most …
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Clearing financial network and its stability
… upon which we will take a look at the aspect of large deviation principle of the sequence with appropriate random settings. In the second part, we also consider an operation, called novation, which changes the topology of a financial network and hence its stability. However, the stability in this …
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The Reflected Quasipotential: Characterization and Exploration
… of reflected Brownian motion satisfy a large deviation principle (with respect to a spatial scaling parameter) with V(x) as the rate function. The Skorokhod Problem is an essential device in the construction and analysis of reflected Brownian motion and our value function V(x). Here we …
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Fluctuation Relations for Stochastic Systems far from Equilibrium
… probability distributions are the result of a large number of repetitions of the same experiment. Due to the small scale of these experiments, the outcome can vary significantly from one realization to the next. Strong theoretical predictions exist, collectively called Fluctuation Theorems, …
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Random geometry in two and three dimensions
… In the first half of this thesis, we prove a large deviation principle for dimer tilings in three dimensions. This generalizes a two-dimensional result of Cohn, Kenyon, and Propp, and is one of the first results for dimers in any dimension d > 2. Many ideas and constructions used to study …
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Advanced approaches to ruin probability and novel extensions of Hoeffding Inequalities in insurance mathematics
… random variables, and the criticality of large deviation inequalities. Moreover, the synthesis of past methodologies with the latest techniques has enabled a more comprehensive understanding of exponentially decaying inequalities. The thesis provides a thorough literature review, …
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Finite time suboptimal control design of nonlinear systems with θ-D technique and implementation to aerospace applications
… the advantages of the perturbation terms, the large control was not required to cope with the large deviation at the initial time, which alleviates the severe tests of the actuators. The detailed procedure to develop this technique and corresponding stability proof were provided. The …
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Dynamical approach in quantum information theory
Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2025-08-01
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Fine properties of stochastic evolution equations and their applications
… small multiplicative noise. A Freidlin-Wentzell large deviation principle is established for the distributions of solutions to a large class of SPDE, which include all stochastic evolution equations with monotone coefficients. In the second part, some properties of invariant measures and …
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Dynamical large deviations and phase separation in systems of interacting particles
We study large deviations in the clustering of diffusing systems, mainly through the lens of macroscopic fluctuation theory (MFT). Additionally we study optimal control forces in such ensembles. First, we consider a one dimensional system of hard-core diffusing particles and focus on the large …
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Oscillation of quenched slowdown asymptotics of random walks in random environment in Z
<p>We consider a one dimensional random walk in a random environment (RWRE) with a positive speed lim<em>n</em>→∞ (<em>Xn/</em>) = υα > 0. Gantert and Zeitouni showed that if the environment has both positive and negative local drifts then the quenched slowdown probabilities <em>P</em> …
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